Calculate the percentage error between a measured (experimental) value and a true (theoretical) value.
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Percentage error is a measure used mainly in science and laboratory experiments to determine how accurate a measured or experimental value is compared to the previously known theoretical or true value. It's calculated by subtracting the true value from the experimental value, taking the absolute value of the difference, then dividing it by the absolute true value, and multiplying the result by 100. The closer the percentage error is to zero, the more accurate and closer to the expected true value the experimental measurements are. This calculator is widely used in physics and chemistry labs to assess the accuracy of instruments and experiments, as well as in any field that requires comparing a measured result to a known reference value. Because the absolute value is taken before dividing, the reported percentage error always describes the size of the deviation only, leaving the direction of the error to be noted separately when that detail matters.
Every physical measurement carries some amount of error, whether from instrument limitations, human reading precision, or unavoidable environmental variation. Percentage error is the standard way scientists communicate how significant that error actually is, because a raw numerical difference on its own says almost nothing about accuracy without context.
Consider two experiments: one measures a value as being off by 2 grams, and another is off by 2 grams as well. If the true value in the first experiment is 10 grams, an error of 2 grams is a serious 20% deviation. If the true value in the second is 2,000 grams, the same 2-gram error represents just 0.1% — a nearly perfect result. Reporting only 'off by 2 grams' hides this enormous difference in actual precision, which is exactly why percentage error, not the raw difference, is the figure that appears in lab reports and published research.
The formula's use of an absolute value in the numerator is a deliberate simplification. Without it, an experimental value below the true value would produce a negative error, and one above it would produce a positive error — useful information in some contexts, but often unnecessary noise when the only question is 'how far off was this measurement, in general'. Some laboratory courses do ask students to report the signed version (sometimes called percent deviation) specifically to track whether an instrument consistently reads high or low, which is a different and complementary piece of information from percentage error alone.
In educational settings, percentage error calculations are a standard part of physics and chemistry lab reports, used to evaluate anything from a measured gravitational acceleration (compared against the accepted 9.81 m/s²) to a titration's measured concentration compared against a known standard solution. A percentage error under roughly 5% is often treated as acceptable for typical classroom lab equipment, though the acceptable threshold varies significantly by field, instrument quality, and the specific experiment being performed.
Outside formal science, the same calculation underlies quality control in manufacturing (comparing a produced part's dimensions against its design specification), estimation exercises (comparing a guessed value against the actual outcome), and any situation where a predicted or measured number needs to be judged against a known correct answer rather than simply reported on its own.
It depends on the field, but generally the closer to 0%, the more accurate the measurement — under 5% is often considered good in many school experiments.
The standard formula always uses the absolute value, so the result shown is a non-negative percentage.
Percentage error compares a measured value to a known true value, while percentage change compares two values over time or conditions.